From its earlier adoption in JPEG to its recent application in HEVC (High Efficiency Video Coding), the newest video coding standard [3], the discrete cosine transform (DCT) has been widely applied in digital signal processing, particularly in lossy image and video coding. It has thus attracted, during the past few decades, a lot of interest in understanding the statistical distribution of DCT coefficients (see, for example, [1], [4], [7], [9], and references therein). Deep and accurate understanding of the distribution of DCT coefficients would be useful to quantization design [12], entropy coding, rate control [7], image understanding and enhancement [1], and image and video analytics [13] in general.
In the literature, Laplacian distributions, Cauchy distributions, Gaussian distributions, mixtures thereof, and generalized Gaussian (GG) distributions have all been suggested to model the distribution of DCT coefficients (see, for example, [2], [4], [9], and references therein). Depending on the actual image data sources used and the need to balance modeling accuracy and model's simplicity/practicality, each of these models may be justified to some degree for some specific application. In general, it is believed that in terms of modeling accuracy, GG distributions with a shape parameter and a scale parameter achieve the best performance [2][9]. However, parameter estimation for GG distributions is difficult and hence the applicability of the GG model to applications, particularly online applications, may be limited. On the other hand, the Laplacian model has been found to balance well between complexity and modeling accuracy; it has been widely adopted in image and video coding [12], although its modeling accuracy is significantly inferior to that of the GG model [2].